The field of modulational instability (MI) and rogue waves (RWs) has considered one of the
most interdisciplinary areas of research enclosing plasma physics [1]}, oceanography [2]},
Bose-Einstein condensation [3]}, optics [4]}, superfluid helium [5]}, and
even finance [6]} . Researchers have devoted their attention to solve the mystery of this
colossal waves due to the intrinsically arbitrary nature, and the complex formation mechanisms. Recently,
a number of authors have studied different criteria of MI and RWs in space and laboratory plasmas.
Bains et al. [7]} studied the MI of IAWs with a \(q\) -distributed electrons,
and found that the stable domain for IAWs increases with \(q\)  within sub-extensive limit.
Abdelwahed et al. [8]} studied IA RWs (IARWs) in PIP in presence of super-thermal
electrons. Elwakil et al. [9]} analyzed the effects of non-thermal electrons
on MI conditions of IAWs, and observed that electrons non-thermality reduces the critical wave
number (\(k_c\) ) in PIP. El-Labany et al. [10]} have derived the nonlinear
Schrödinger equation (NLSE) in a three component PIP in presence of iso-thermal electrons, and
observed that the number density of the negative ions enhances the amplitude of the IARWs. In our
present investigation, we have extended the previous work of El-Labany et al. [10]}
by considering adiabatic pressure of the PI in four component (comprising \(q\) -distributed electrons and positrons, adiabatic
positive and negative ions) PIP, and also will examine the effects of the plasma parameters on the MI of IAWs,
and the formation of the IARWS.
